why is it that so 5pi612 but sin112 does not5pi6SolutionDoma

why is it that so 5pi/6=1/2, but sin^-1(1/2) does not=5pi/6?

Solution

Domain and Range of all inverse trigonometric functionis always defined between some interval so that inverse function exist

And range of sin^-1 function is [-pi/2 , pi/2] so for sin^-1 function the answer always lies between [-pi/2,pi/2] since it convers all domain from [-1,1]